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<div class="header">
  <div class="headertitle">
<div class="title">std::ratio&lt; Num, Denom &gt; Class Template Reference<div class="ingroups"><a class="el" href="group__group-ext.html">External adapters</a> &raquo; <a class="el" href="group__group-ext-std.html">Standard library adapters</a></div></div>  </div>
</div><!--header-->
<div class="contents">
<a name="details" id="details"></a><h2 class="groupheader">Description</h2>
<div class="textblock"><h3>template&lt;std::intmax_t Num, std::intmax_t Denom&gt;<br />
class std::ratio&lt; Num, Denom &gt;</h3>

<p>Adaptation of <code><a class="el" href="classstd_1_1ratio.html" title="Adaptation of std::ratio for Hana.">std::ratio</a></code> for Hana. </p>
<h2><a class="anchor" id="autotoc_md18"></a>
Modeled concepts</h2>
<ol type="1">
<li><code>Comparable</code><br  />
<code><a class="el" href="classstd_1_1ratio.html" title="Adaptation of std::ratio for Hana.">std::ratio</a></code>s are compared for equality using <code>std::ratio_equal</code>. <div class="fragment"><div class="line"><span class="comment">// Copyright Louis Dionne 2013-2017</span></div>
<div class="line"><span class="comment">// Distributed under the Boost Software License, Version 1.0.</span></div>
<div class="line"><span class="comment">// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)</span></div>
<div class="line"> </div>
<div class="line"><span class="preprocessor">#include &lt;<a class="code" href="assert_8hpp.html">boost/hana/assert.hpp</a>&gt;</span></div>
<div class="line"><span class="preprocessor">#include &lt;<a class="code" href="equal_8hpp.html">boost/hana/equal.hpp</a>&gt;</span></div>
<div class="line"><span class="preprocessor">#include &lt;<a class="code" href="ratio_8hpp.html">boost/hana/ext/std/ratio.hpp</a>&gt;</span></div>
<div class="line"><span class="preprocessor">#include &lt;<a class="code" href="not__equal_8hpp.html">boost/hana/not_equal.hpp</a>&gt;</span></div>
<div class="line"> </div>
<div class="line"><span class="preprocessor">#include &lt;ratio&gt;</span></div>
<div class="line"><span class="keyword">namespace </span>hana = <a class="code" href="namespaceboost_1_1hana.html">boost::hana</a>;</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"><a class="code" href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a>(<a class="code" href="group__group-_comparable.html#gacaf1ebea6b3ab96ac9dcb82f0e64e547">hana::equal</a>(<a class="code" href="classstd_1_1ratio.html">std::ratio&lt;3, 4&gt;</a>{}, <a class="code" href="classstd_1_1ratio.html">std::ratio&lt;15, 20&gt;</a>{}));</div>
<div class="line"><a class="code" href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a>(<a class="code" href="group__group-_comparable.html#gae33be2e0d5e04f19082f4b7740dfc9cd">hana::not_equal</a>(<a class="code" href="classstd_1_1ratio.html">std::ratio&lt;3, 4&gt;</a>{}, <a class="code" href="classstd_1_1ratio.html">std::ratio&lt;3, 5&gt;</a>{}));</div>
<div class="line"> </div>
<div class="line"><span class="keywordtype">int</span> main() { }</div>
<div class="ttc" id="aassert_8hpp_html"><div class="ttname"><a href="assert_8hpp.html">assert.hpp</a></div><div class="ttdoc">Defines macros to perform different kinds of assertions.</div></div>
<div class="ttc" id="aclassstd_1_1ratio_html"><div class="ttname"><a href="classstd_1_1ratio.html">std::ratio</a></div><div class="ttdoc">Adaptation of std::ratio for Hana.</div><div class="ttdef"><b>Definition:</b> ratio.hpp:58</div></div>
<div class="ttc" id="aequal_8hpp_html"><div class="ttname"><a href="equal_8hpp.html">equal.hpp</a></div><div class="ttdoc">Defines boost::hana::equal.</div></div>
<div class="ttc" id="agroup__group-_comparable_html_gacaf1ebea6b3ab96ac9dcb82f0e64e547"><div class="ttname"><a href="group__group-_comparable.html#gacaf1ebea6b3ab96ac9dcb82f0e64e547">boost::hana::equal</a></div><div class="ttdeci">constexpr auto equal</div><div class="ttdoc">Returns a Logical representing whether x is equal to y.</div><div class="ttdef"><b>Definition:</b> equal.hpp:64</div></div>
<div class="ttc" id="agroup__group-_comparable_html_gae33be2e0d5e04f19082f4b7740dfc9cd"><div class="ttname"><a href="group__group-_comparable.html#gae33be2e0d5e04f19082f4b7740dfc9cd">boost::hana::not_equal</a></div><div class="ttdeci">constexpr auto not_equal</div><div class="ttdoc">Returns a Logical representing whether x is not equal to y.</div><div class="ttdef"><b>Definition:</b> not_equal.hpp:54</div></div>
<div class="ttc" id="agroup__group-assertions_html_ga2c5006540936d9f8880e3a39f4fcc035"><div class="ttname"><a href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a></div><div class="ttdeci">#define BOOST_HANA_CONSTANT_CHECK(...)</div><div class="ttdoc">Equivalent to BOOST_HANA_CONSTANT_ASSERT, but not influenced by the BOOST_HANA_CONFIG_DISABLE_ASSERTI...</div><div class="ttdef"><b>Definition:</b> assert.hpp:239</div></div>
<div class="ttc" id="anamespaceboost_1_1hana_html"><div class="ttname"><a href="namespaceboost_1_1hana.html">boost::hana</a></div><div class="ttdoc">Namespace containing everything in the library.</div><div class="ttdef"><b>Definition:</b> accessors.hpp:20</div></div>
<div class="ttc" id="anot__equal_8hpp_html"><div class="ttname"><a href="not__equal_8hpp.html">not_equal.hpp</a></div><div class="ttdoc">Defines boost::hana::not_equal.</div></div>
<div class="ttc" id="aratio_8hpp_html"><div class="ttname"><a href="ratio_8hpp.html">ratio.hpp</a></div><div class="ttdoc">Adapts std::ratio for use with Hana.</div></div>
</div><!-- fragment --></li>
<li><code>Orderable</code><br  />
<code><a class="el" href="classstd_1_1ratio.html" title="Adaptation of std::ratio for Hana.">std::ratio</a></code>s are ordered using <code>std::ratio_less</code>. <div class="fragment"><div class="line"><span class="comment">// Copyright Louis Dionne 2013-2017</span></div>
<div class="line"><span class="comment">// Distributed under the Boost Software License, Version 1.0.</span></div>
<div class="line"><span class="comment">// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)</span></div>
<div class="line"> </div>
<div class="line"><span class="preprocessor">#include &lt;<a class="code" href="assert_8hpp.html">boost/hana/assert.hpp</a>&gt;</span></div>
<div class="line"><span class="preprocessor">#include &lt;<a class="code" href="ratio_8hpp.html">boost/hana/ext/std/ratio.hpp</a>&gt;</span></div>
<div class="line"><span class="preprocessor">#include &lt;<a class="code" href="less_8hpp.html">boost/hana/less.hpp</a>&gt;</span></div>
<div class="line"><span class="preprocessor">#include &lt;<a class="code" href="less__equal_8hpp.html">boost/hana/less_equal.hpp</a>&gt;</span></div>
<div class="line"> </div>
<div class="line"><span class="preprocessor">#include &lt;ratio&gt;</span></div>
<div class="line"><span class="keyword">namespace </span>hana = <a class="code" href="namespaceboost_1_1hana.html">boost::hana</a>;</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"><a class="code" href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a>(<a class="code" href="group__group-_orderable.html#gad510011602bdb14686f1c4ec145301c9">hana::less</a>(<a class="code" href="classstd_1_1ratio.html">std::ratio&lt;3, 12&gt;</a>{}, <a class="code" href="classstd_1_1ratio.html">std::ratio&lt;5, 12&gt;</a>{}));</div>
<div class="line"><a class="code" href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a>(<a class="code" href="group__group-_orderable.html#ga9917dd82beb67151bf5657245d37b851">hana::less_equal</a>(<a class="code" href="classstd_1_1ratio.html">std::ratio&lt;6, 12&gt;</a>{}, <a class="code" href="classstd_1_1ratio.html">std::ratio&lt;4, 8&gt;</a>{}));</div>
<div class="line"> </div>
<div class="line"><span class="keywordtype">int</span> main() { }</div>
<div class="ttc" id="agroup__group-_orderable_html_ga9917dd82beb67151bf5657245d37b851"><div class="ttname"><a href="group__group-_orderable.html#ga9917dd82beb67151bf5657245d37b851">boost::hana::less_equal</a></div><div class="ttdeci">constexpr auto less_equal</div><div class="ttdoc">Returns a Logical representing whether x is less than or equal to y.</div><div class="ttdef"><b>Definition:</b> less_equal.hpp:38</div></div>
<div class="ttc" id="agroup__group-_orderable_html_gad510011602bdb14686f1c4ec145301c9"><div class="ttname"><a href="group__group-_orderable.html#gad510011602bdb14686f1c4ec145301c9">boost::hana::less</a></div><div class="ttdeci">constexpr auto less</div><div class="ttdoc">Returns a Logical representing whether x is less than y.</div><div class="ttdef"><b>Definition:</b> less.hpp:37</div></div>
<div class="ttc" id="aless_8hpp_html"><div class="ttname"><a href="less_8hpp.html">less.hpp</a></div><div class="ttdoc">Defines boost::hana::less.</div></div>
<div class="ttc" id="aless__equal_8hpp_html"><div class="ttname"><a href="less__equal_8hpp.html">less_equal.hpp</a></div><div class="ttdoc">Defines boost::hana::less_equal.</div></div>
</div><!-- fragment --></li>
<li><code>Monoid</code>, <code>Group</code>, <code>Ring</code>, and <code>EuclideanRing</code><br  />
<code><a class="el" href="classstd_1_1ratio.html" title="Adaptation of std::ratio for Hana.">std::ratio</a></code>s are added, subtracted, multiplied and divided using <code>std::ratio_add</code>, <code>std::ratio_subtract</code>, <code>std::ratio_multiply</code> and <code>std::ratio_divide</code>, respectively. Furthermore, the neutral element for the additive operation is <code><a class="el" href="classstd_1_1ratio.html" title="Adaptation of std::ratio for Hana.">std::ratio</a>&lt;0, 1&gt;{}</code>, and the neutral element for the multiplicative operation is <code><a class="el" href="classstd_1_1ratio.html" title="Adaptation of std::ratio for Hana.">std::ratio</a>&lt;1, 1&gt;{}</code>. <div class="fragment"><div class="line"><span class="comment">// Copyright Louis Dionne 2013-2017</span></div>
<div class="line"><span class="comment">// Distributed under the Boost Software License, Version 1.0.</span></div>
<div class="line"><span class="comment">// (See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)</span></div>
<div class="line"> </div>
<div class="line"><span class="preprocessor">#include &lt;<a class="code" href="assert_8hpp.html">boost/hana/assert.hpp</a>&gt;</span></div>
<div class="line"><span class="preprocessor">#include &lt;<a class="code" href="div_8hpp.html">boost/hana/div.hpp</a>&gt;</span></div>
<div class="line"><span class="preprocessor">#include &lt;<a class="code" href="equal_8hpp.html">boost/hana/equal.hpp</a>&gt;</span></div>
<div class="line"><span class="preprocessor">#include &lt;<a class="code" href="ratio_8hpp.html">boost/hana/ext/std/ratio.hpp</a>&gt;</span></div>
<div class="line"><span class="preprocessor">#include &lt;<a class="code" href="minus_8hpp.html">boost/hana/minus.hpp</a>&gt;</span></div>
<div class="line"><span class="preprocessor">#include &lt;<a class="code" href="mod_8hpp.html">boost/hana/mod.hpp</a>&gt;</span></div>
<div class="line"><span class="preprocessor">#include &lt;<a class="code" href="mult_8hpp.html">boost/hana/mult.hpp</a>&gt;</span></div>
<div class="line"><span class="preprocessor">#include &lt;<a class="code" href="one_8hpp.html">boost/hana/one.hpp</a>&gt;</span></div>
<div class="line"><span class="preprocessor">#include &lt;<a class="code" href="plus_8hpp.html">boost/hana/plus.hpp</a>&gt;</span></div>
<div class="line"><span class="preprocessor">#include &lt;<a class="code" href="zero_8hpp.html">boost/hana/zero.hpp</a>&gt;</span></div>
<div class="line"> </div>
<div class="line"><span class="preprocessor">#include &lt;ratio&gt;</span></div>
<div class="line"><span class="keyword">namespace </span>hana = <a class="code" href="namespaceboost_1_1hana.html">boost::hana</a>;</div>
<div class="line"> </div>
<div class="line"> </div>
<div class="line"><a class="code" href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a>(<a class="code" href="group__group-_comparable.html#gacaf1ebea6b3ab96ac9dcb82f0e64e547">hana::equal</a>(</div>
<div class="line">    <a class="code" href="group__group-_monoid.html#gaeb5d4a1e967e319712f9e4791948896c">hana::plus</a>(<a class="code" href="classstd_1_1ratio.html">std::ratio&lt;5, 3&gt;</a>{}, <a class="code" href="classstd_1_1ratio.html">std::ratio&lt;3, 12&gt;</a>{}),</div>
<div class="line">    <a class="code" href="classstd_1_1ratio.html">std::ratio&lt;23, 12&gt;</a>{}</div>
<div class="line">));</div>
<div class="line"> </div>
<div class="line"><a class="code" href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a>(<a class="code" href="group__group-_comparable.html#gacaf1ebea6b3ab96ac9dcb82f0e64e547">hana::equal</a>(</div>
<div class="line">    <a class="code" href="group__group-_group.html#ga2020c526324f361a2b990fe8d1b07c20">hana::minus</a>(<a class="code" href="classstd_1_1ratio.html">std::ratio&lt;5, 3&gt;</a>{}, <a class="code" href="classstd_1_1ratio.html">std::ratio&lt;3, 13&gt;</a>{}),</div>
<div class="line">    <a class="code" href="classstd_1_1ratio.html">std::ratio&lt;56, 39&gt;</a>{}</div>
<div class="line">));</div>
<div class="line"> </div>
<div class="line"><a class="code" href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a>(<a class="code" href="group__group-_comparable.html#gacaf1ebea6b3ab96ac9dcb82f0e64e547">hana::equal</a>(</div>
<div class="line">    <a class="code" href="group__group-_ring.html#ga052d31c269a6a438cc8004c9ad1efdfa">hana::mult</a>(<a class="code" href="classstd_1_1ratio.html">std::ratio&lt;5, 3&gt;</a>{}, <a class="code" href="classstd_1_1ratio.html">std::ratio&lt;3, 13&gt;</a>{}),</div>
<div class="line">    <a class="code" href="classstd_1_1ratio.html">std::ratio&lt;15, 39&gt;</a>{}</div>
<div class="line">));</div>
<div class="line"> </div>
<div class="line"><a class="code" href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a>(<a class="code" href="group__group-_comparable.html#gacaf1ebea6b3ab96ac9dcb82f0e64e547">hana::equal</a>(</div>
<div class="line">    <a class="code" href="group__group-_euclidean_ring.html#ga4225a7988ce98903228913dde53762df">hana::div</a>(<a class="code" href="classstd_1_1ratio.html">std::ratio&lt;5, 3&gt;</a>{}, <a class="code" href="classstd_1_1ratio.html">std::ratio&lt;3, 13&gt;</a>{}),</div>
<div class="line">    <a class="code" href="classstd_1_1ratio.html">std::ratio&lt;65, 9&gt;</a>{}</div>
<div class="line">));</div>
<div class="line"> </div>
<div class="line"><span class="comment">// The mod of two ratios is always 0, because they can always be</span></div>
<div class="line"><span class="comment">// divided without remainder.</span></div>
<div class="line"><a class="code" href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a>(<a class="code" href="group__group-_comparable.html#gacaf1ebea6b3ab96ac9dcb82f0e64e547">hana::equal</a>(</div>
<div class="line">    <a class="code" href="group__group-_euclidean_ring.html#ga9b47b223d5b02db933b3c93b5bd1a062">hana::mod</a>(<a class="code" href="classstd_1_1ratio.html">std::ratio&lt;5, 3&gt;</a>{}, <a class="code" href="classstd_1_1ratio.html">std::ratio&lt;3, 13&gt;</a>{}),</div>
<div class="line">    <a class="code" href="classstd_1_1ratio.html">std::ratio&lt;0&gt;</a>{}</div>
<div class="line">));</div>
<div class="line"> </div>
<div class="line"><a class="code" href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a>(<a class="code" href="group__group-_comparable.html#gacaf1ebea6b3ab96ac9dcb82f0e64e547">hana::equal</a>(</div>
<div class="line">    hana::zero&lt;hana::ext::std::ratio_tag&gt;(),</div>
<div class="line">    <a class="code" href="classstd_1_1ratio.html">std::ratio&lt;0&gt;</a>{}</div>
<div class="line">));</div>
<div class="line"> </div>
<div class="line"><a class="code" href="group__group-assertions.html#ga2c5006540936d9f8880e3a39f4fcc035">BOOST_HANA_CONSTANT_CHECK</a>(<a class="code" href="group__group-_comparable.html#gacaf1ebea6b3ab96ac9dcb82f0e64e547">hana::equal</a>(</div>
<div class="line">    hana::one&lt;hana::ext::std::ratio_tag&gt;(),</div>
<div class="line">    <a class="code" href="classstd_1_1ratio.html">std::ratio&lt;1&gt;</a>{}</div>
<div class="line">));</div>
<div class="line"> </div>
<div class="line"><span class="keywordtype">int</span> main() { }</div>
<div class="ttc" id="adiv_8hpp_html"><div class="ttname"><a href="div_8hpp.html">div.hpp</a></div><div class="ttdoc">Defines boost::hana::div.</div></div>
<div class="ttc" id="agroup__group-_euclidean_ring_html_ga4225a7988ce98903228913dde53762df"><div class="ttname"><a href="group__group-_euclidean_ring.html#ga4225a7988ce98903228913dde53762df">boost::hana::div</a></div><div class="ttdeci">constexpr auto div</div><div class="ttdoc">Generalized integer division.</div><div class="ttdef"><b>Definition:</b> div.hpp:43</div></div>
<div class="ttc" id="agroup__group-_euclidean_ring_html_ga9b47b223d5b02db933b3c93b5bd1a062"><div class="ttname"><a href="group__group-_euclidean_ring.html#ga9b47b223d5b02db933b3c93b5bd1a062">boost::hana::mod</a></div><div class="ttdeci">constexpr auto mod</div><div class="ttdoc">Generalized integer modulus.</div><div class="ttdef"><b>Definition:</b> mod.hpp:46</div></div>
<div class="ttc" id="agroup__group-_group_html_ga2020c526324f361a2b990fe8d1b07c20"><div class="ttname"><a href="group__group-_group.html#ga2020c526324f361a2b990fe8d1b07c20">boost::hana::minus</a></div><div class="ttdeci">constexpr auto minus</div><div class="ttdoc">Subtract two elements of a group.</div><div class="ttdef"><b>Definition:</b> minus.hpp:51</div></div>
<div class="ttc" id="agroup__group-_monoid_html_gaeb5d4a1e967e319712f9e4791948896c"><div class="ttname"><a href="group__group-_monoid.html#gaeb5d4a1e967e319712f9e4791948896c">boost::hana::plus</a></div><div class="ttdeci">constexpr auto plus</div><div class="ttdoc">Associative binary operation on a Monoid.</div><div class="ttdef"><b>Definition:</b> plus.hpp:47</div></div>
<div class="ttc" id="agroup__group-_ring_html_ga052d31c269a6a438cc8004c9ad1efdfa"><div class="ttname"><a href="group__group-_ring.html#ga052d31c269a6a438cc8004c9ad1efdfa">boost::hana::mult</a></div><div class="ttdeci">constexpr auto mult</div><div class="ttdoc">Associative operation of a Ring.</div><div class="ttdef"><b>Definition:</b> mult.hpp:47</div></div>
<div class="ttc" id="aminus_8hpp_html"><div class="ttname"><a href="minus_8hpp.html">minus.hpp</a></div><div class="ttdoc">Defines boost::hana::minus.</div></div>
<div class="ttc" id="amod_8hpp_html"><div class="ttname"><a href="mod_8hpp.html">mod.hpp</a></div><div class="ttdoc">Defines boost::hana::mod.</div></div>
<div class="ttc" id="amult_8hpp_html"><div class="ttname"><a href="mult_8hpp.html">mult.hpp</a></div><div class="ttdoc">Defines boost::hana::mult.</div></div>
<div class="ttc" id="aone_8hpp_html"><div class="ttname"><a href="one_8hpp.html">one.hpp</a></div><div class="ttdoc">Defines boost::hana::one.</div></div>
<div class="ttc" id="aplus_8hpp_html"><div class="ttname"><a href="plus_8hpp.html">plus.hpp</a></div><div class="ttdoc">Defines boost::hana::plus.</div></div>
<div class="ttc" id="azero_8hpp_html"><div class="ttname"><a href="zero_8hpp.html">zero.hpp</a></div><div class="ttdoc">Defines boost::hana::zero.</div></div>
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